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Expander Graphs and their Applications
, 2003
"... Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . ..."
Abstract

Cited by 188 (5 self)
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Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Derandomizing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Magical Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 A Super Concentrator with O(n) edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Derandomizing Random Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
RAMBO: A Reconfigurable Atomic Memory Service for Dynamic Networks
 In DISC
, 2002
"... This paper presents an algorithm that emulates atomic read/write shared objects in a dynamic network setting. To ensure availability and faulttolerance, the objects are replicated. To ensure atomicity, reads and writes are performed using quorum configurations, each of which consists of a set of me ..."
Abstract

Cited by 94 (12 self)
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This paper presents an algorithm that emulates atomic read/write shared objects in a dynamic network setting. To ensure availability and faulttolerance, the objects are replicated. To ensure atomicity, reads and writes are performed using quorum configurations, each of which consists of a set of members plus sets of readquorums and writequorums. The algorithm is reconfigurable: the quorum configurations may change during computation, and such changes do not cause violations of atomicity. Any quorum configuration may be installed at any time. The algorithm tolerates processor stopping failure and message loss. The algorithm performs three major tasks, all concurrently: reading and writing objects, introducing new configurations, and "garbagecollecting" obsolete configurations.
Dispersers, Deterministic Amplification, and Weak Random Sources.
, 1989
"... We use a certain type of expanding bipartite graphs, called disperser graphs, to design procedures for picking highly correlated samples from a finite set, with the property that the probability of hitting any sufficiently large subset is high. These procedures require a relatively small number of r ..."
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Cited by 93 (11 self)
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We use a certain type of expanding bipartite graphs, called disperser graphs, to design procedures for picking highly correlated samples from a finite set, with the property that the probability of hitting any sufficiently large subset is high. These procedures require a relatively small number of random bits and are robust with respect to the quality of the random bits. Using these sampling procedures to sample random inputs of polynomial time probabilistic algorithms, we can simulate the performance of some probabilistic algorithms with less random bits or with low quality random bits. We obtain the following results: 1. The error probability of an RP or BPP algorithm that operates with a constant error bound and requires n random bits, can be made exponentially small (i.e. 2 \Gamman ), with only (3 + ffl)n random bits, as opposed to standard amplification techniques that require \Omega\Gamma n 2 ) random bits for the same task. This result is nearly optimal, since the informati...
Distributed programming with shared data
 Computer Languages
, 1988
"... Until recently, at least one thing was clear about parallel programming: tightly coupled (shared memory) machines were programmed in a language based on shared variables and loosely coupled (distributed) systems were programmed using message passing. The explosive growth of research on distributed s ..."
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Cited by 80 (15 self)
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Until recently, at least one thing was clear about parallel programming: tightly coupled (shared memory) machines were programmed in a language based on shared variables and loosely coupled (distributed) systems were programmed using message passing. The explosive growth of research on distributed systems and their languages, however, has led to several new methodologies that blur this simple distinction. Operating system primitives (e.g., problemoriented shared memory, Shared Virtual Memory, the Agora shared memory) and languages (e.g., Concurrent Prolog, Linda, Emerald) for programming distributed systems have been proposed that support the shared variable paradigm without the presence of physical shared memory. In this paper we will look at the reasons for this evolution, the resemblances and differences among these new proposals, and the key issues in their design and implementation. It turns out that many implementations are based on replication of data. We take this idea one step further, and discuss how automatic replication (initiated by the run time system) can be used as a basis for a new model, called the shared dataobject model, whose semantics are similar to the shared variable model. Finally, we discuss the design of a new language for distributed programming, Orca, based on the shared dataobject model. 1.
Optical Communication for Pointer Based Algorithms
, 1988
"... ) Abstract In this paper we study the Local Memory PRAM. This model allows unit cost communication but assumes that the shared memory is divided into modules. This model is motivated by a consideration of potential optical computers. We show that fundamental problems such as listranking and parall ..."
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Cited by 53 (1 self)
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) Abstract In this paper we study the Local Memory PRAM. This model allows unit cost communication but assumes that the shared memory is divided into modules. This model is motivated by a consideration of potential optical computers. We show that fundamental problems such as listranking and parallel tree contraction can be implemented on this model in O(log n) time using n= log n processors. To solve the listranking problem we introduce a general asynchronous technique which has relevance to a number of problems. 1 Introduction We consider a model of parallel computation that is especially suited to pointer based computation. We motivate this model by showing that basic problems, like listranking and parallel tree contraction, can be performed in O(log n) time using only n= log n processors. We also show that any step on this model can be simulated in unit time on this model by a machine with an optical communication architecture. Thus we contend that the basic problem of listra...
GeoQuorums: Implementing Atomic Memory in Mobile Ad Hoc Networks
, 2004
"... We present a new approach, the GeoQuorums approach, for implementing atomic read/write shared memory in mobile ad hoc networks. Our approach is based on associating abstract atomic objects with certain geographic locations. We assume the existence of focal points, geographic areas that are normall ..."
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Cited by 51 (12 self)
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We present a new approach, the GeoQuorums approach, for implementing atomic read/write shared memory in mobile ad hoc networks. Our approach is based on associating abstract atomic objects with certain geographic locations. We assume the existence of focal points, geographic areas that are normally "populated" by mobile nodes.
Horizons of Parallel Computation
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1993
"... This paper considers the ultimate impact of fundamental physical limitationsnotably, speed of light and device sizeon parallel computing machines. Although we fully expect an innovative and very gradual evolution to the limiting situation, we take here the provocative view of exploring the ..."
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Cited by 39 (3 self)
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This paper considers the ultimate impact of fundamental physical limitationsnotably, speed of light and device sizeon parallel computing machines. Although we fully expect an innovative and very gradual evolution to the limiting situation, we take here the provocative view of exploring the consequences of the accomplished attainment of the physical bounds. The main result is that scalability holds only for neighborly interconnections, such as the square mesh, of boundedsize synchronous modules, presumably of the areauniversal type. We also discuss the ultimate infeasibility of latencyhiding, the violation of intuitive maximal speedups, and the emerging novel processortime tradeoffs.
On Contention Resolution Protocols and Associated Probabilistic Phenomena
 IN PROCEEDINGS OF THE 26TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1994
"... ..."
Exploiting Storage Redundancy to Speed Up Randomized Shared Memory Simulations
 IN PROCEEDINGS OF THE 12TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1996
"... Assume that a set U of memory locations is distributed among n memory modules, using some number a of hash functions h1 ; : : : ; ha , randomly and independently drawn from a high performance universal class of hash functions. Thus each memory location has a copies. Consider the task of accessing b ..."
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Cited by 33 (9 self)
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Assume that a set U of memory locations is distributed among n memory modules, using some number a of hash functions h1 ; : : : ; ha , randomly and independently drawn from a high performance universal class of hash functions. Thus each memory location has a copies. Consider the task of accessing b out of the a copies for each of given keys x1 ; : : : ; xn 2 U , b ! a. The paper presents and analyses a simple process executing the above task on distributed memory machines (DMMs) with n processors. Efficient implementations are presented, implying ffl a simulation of an nprocessor PRAM on an nprocessor optical crossbar DMM with delay O(log log n), ffl a simulation as above on an arbitraryDMM with delay O( log log n log log log n ), ffl an implementation of a static dictionary on an arbitraryDMM with parallel access time O(log n + log log n log a ), if a hash functions are used. In particular, an access time of O(log n) can be reached if (log n) 1= log n hash funct...
The Complexity of Computation on the Parallel Random Access Machine
, 1993
"... PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much m ..."
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Cited by 32 (4 self)
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PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much more powerful than restricted instruction set PRAMs. THEOREM 21.16 Any function of n variables can be computed by an abstract EROW PRAM in O(log n) steps using n= log 2 n processors and n=2 log 2 n shared memory cells. PROOF Each processor begins by reading log 2 n input values and combining them into one large value. The information known by processors are combined in a binarytreelike fashion. In each round, the remaining processors are grouped into pairs. In each pair, one processor communicates the information it knows about the input to the other processor and then leaves the computation. After dlog 2 ne rounds, one processor knows all n input values. Then this processor computes th...